Finite Group Databasebeta

← C43×#25508 #24945525

Subgroups — C43×#25508 #24945525

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#540C211yesmaximal, characteristic, complemented
2C2×C43×#469C211yesmaximal, characteristic, complemented
3C2×C43×#466C211yesmaximal, characteristic, complemented
4C43×#2624C211yesmaximal, characteristic, complemented
5C43×#2059C211yesmaximal, characteristic, complemented
6C43×#2041C211yesmaximal, characteristic, complemented
7C43×#2025C211yesmaximal, characteristic, complemented
8C43×#2011C211yesmaximal, characteristic, complemented
9C43×#1895C211yesmaximal, characteristic, complemented
10C43×#1893C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1879C211yesmaximal, characteristic, complemented
13C43×#1864C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic, complemented
15C43×#1729C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C43×#540—24no—
21C43×#540—24no—
22C2×#127×C43C2211yescharacteristic
23C2×#125×C43C2211yescharacteristic
24C2×#123×C43—21no—
25C2×#123×C43—21no—
26C2×#121×C43—21no—
27C2×#121×C43—21no—
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4×D4×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C43×#469—24no—
35C43×#466—24no—
36C2×#107×C43C2211yescharacteristic
37C2×#106×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C43×#399—21no—
47C43×#397—21no—
48C43×#394—21no—
49C43×#394—21no—
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43C2311yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C22×D4×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C2×D8×C43—22no—
75C2×D8×C43—22no—
76C2×D8×C43—22no—
77C2×D8×C43—22no—
78C2×D8×C43—41no—
79C2×D8×C43—41no—
80C2×M16×C43—22no—
81C2×M16×C43—22no—
82C2×M16×C43—41no—
83C22×C8×C43—22no—
84C22×C8×C43—22no—
85C22×C8×C43—41no—
86C22×C8×C43C2311yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90#127×C43—22no—
91#127×C43—22no—
92#125×C43—22no—
93#125×C43—22no—
94#123×C43—28no—
95#123×C43—28no—
96#121×C43—28no—
97#121×C43—28no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43D414yes—
103#121×C43D414yes—
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108#117×C43—22no—
109#117×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#107×C43—22no—
136#106×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—41no—
144#102×C43—41no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C2×D4×C43—24no—
153C2×D4×C43—24no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—24no—
157C2×D4×C43—24no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—42no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43—81no—
179C2×D4×C43—81no—
180C2×D4×C43—81no—
181C2×D4×C43—81no—
182C2×D4×C43—81no—
183C2×D4×C43C2×D412yes—
184C2×D4×C43C2×D412yes—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—24no—
190C22×C4×C43—24no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—81no—
197C22×C4×C43—81no—
198C22×C4×C43—81no—
199C22×C4×C43—81no—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208D8×C43—44no—
209D8×C43—44no—
210M16×C43—44no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—44no—
222C2×C8×C43#4112yes—
223C2×C8×C43#4112yes—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—22no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—81no—
237C4⋊C4×C43—81no—
238C4⋊C4×C43C2×D412yes—
239C4⋊C4×C43C2×D412yes—
240C22⋊C4×C43—24no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—42no—
247C22⋊C4×C43—81no—
248C22⋊C4×C43—81no—
249C22⋊C4×C43—81no—
250C22⋊C4×C43—81no—
251C22⋊C4×C43—81no—
252C42×C43—21no—
253C42×C43—21no—
254C42×C43—21no—
255C42×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43#12012yes—
284C23×C43C22×D411yescharacteristic
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—84no—
298D4×C43—84no—
299D4×C43—84no—
300D4×C43—84no—
301D4×C43—84no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—84no—
336C2×C4×C43—84no—
337C2×C4×C43#12012yes—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C2×C4×C432−1+411yescharacteristic
344C8×C43—22no—
345C8×C43—22no—
346C8×C43—41no—
347C8×C43—41no—
348#25508C4311yesmaximal, characteristic, direct product factor, Sylow
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43C2×#12011yescharacteristic
378C22×C43#53211yescharacteristic
379C22×C43#53711yescharacteristic
380C22×C43#57611yescharacteristic
381C22×C43#57611yescharacteristic
382C22×C43#57611yescharacteristic
383C22×C43#57711yescharacteristic
384C4×C43—22no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43—42no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—42no—
391C4×C43—81no—
392C4×C43—81no—
393C4×C43—81no—
394C4×C43#54611yescharacteristic
395C4×C43#54611yescharacteristic
396C4×C43#54711yescharacteristic
397C4×C43#54711yescharacteristic
398C2×#540C2×C4311yescharacteristic, complemented
399C2×#469C2×C4311yescharacteristic, complemented
400C2×#466C2×C4311yescharacteristic, complemented
401#2624C2×C4311yescharacteristic, complemented
402#2059C2×C4311yescharacteristic, complemented
403#2041C2×C4311yescharacteristic, complemented
404#2025C2×C4311yescharacteristic, complemented
405#2011C2×C4311yescharacteristic, complemented
406#1895C2×C4311yescharacteristic, complemented
407#1893C2×C4311yescharacteristic, complemented
408#1879C2×C4311yescharacteristic, complemented
409#1879C2×C4311yescharacteristic, complemented
410#1864C2×C4311yescharacteristic, complemented
411#1862C2×C4311yescharacteristic, complemented
412#1729C2×C4311yescharacteristic, complemented
413C2×C43—42no—
414C2×C43—82no—
415C2×C43—82no—
416C2×C43—161no—
417C2×C43#243011yescharacteristic
418C2×C43#300811yescharacteristic
419C2×C43#301211yescharacteristic
420C2×C43#317611yescharacteristic
421C2×C43#317911yescharacteristic
422C2×C43#325711yescharacteristic
423C2×C43#325911yescharacteristic
424C22×D8C22×C4311yescharacteristic
425C22×D8C22×C4311yescharacteristic
426C22×M16C22×C4311yescharacteristic
427C23×C8C22×C4311yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C4311yescharacteristic
431C2×#125C22×C4311yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C4311yescharacteristic
437C2×#121C22×C4311yescharacteristic
438C2×#121C22×C4311yescharacteristic
439C2×C4×D4C22×C4311yescharacteristic
440C2×C4×D4C22×C4311yescharacteristic
441C2×#117C22×C4311yescharacteristic
442#469—24no—
443#466—24no—
444C2×#107C22×C4311yescharacteristic
445C2×#106C22×C4311yescharacteristic
446C2×#102C22×C4311yescharacteristic
447C2×#102C22×C4311yescharacteristic
448C2×#102C22×C4311yescharacteristic
449C2×#102C22×C4311yescharacteristic
450C2×#102C22×C4311yescharacteristic
451C2×#102C22×C4311yescharacteristic
452C2×#102C22×C4311yescharacteristic
453C2×#102C22×C4311yescharacteristic
454#399—21no—
455#397—21no—
456#394—21no—
457#394—21no—
458#390C22×C4311yescharacteristic
459#390C22×C4311yescharacteristic
460#389C22×C4311yescharacteristic
461#389C22×C4311yescharacteristic
462#380C22×C4311yescharacteristic
463#340C22×C4311yescharacteristic
464#340C22×C4311yescharacteristic
465#340C22×C4311yescharacteristic
466#340C22×C4311yescharacteristic
467#336C22×C4311yescharacteristic
468#336C22×C4311yescharacteristic
469#336C22×C4311yescharacteristic
470#336C22×C4311yescharacteristic
471C43#2550811yescharacteristic, direct product factor, Sylow
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C4311yescharacteristic
478C22×D4C23×C4311yescharacteristic
479C22×D4C23×C4311yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C4311yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8—41no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8C23×C4311yescharacteristic
496C22×C8C23×C4311yescharacteristic
497C22×C8C23×C4311yescharacteristic
498C22×C8C23×C4311yescharacteristic
499#127—22no—
500#127—22no—
501#125—22no—
502#125—22no—
503#123—28no—
504#123—28no—
505#121—28no—
506#121—28no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121D4×C4314yes—
512#121D4×C4314yes—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C4311yescharacteristic
524C2×C4⋊C4D4×C4311yescharacteristic
525C2×C4⋊C4C23×C4311yescharacteristic
526C2×C4⋊C4C23×C4311yescharacteristic
527C2×C4⋊C4C23×C4311yescharacteristic
528C2×C4⋊C4C23×C4311yescharacteristic
529C2×C4⋊C4C23×C4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4D4×C4311yescharacteristic
541C2×C22⋊C4D4×C4311yescharacteristic
542C2×C42C23×C4311yescharacteristic
543C2×C42C23×C4311yescharacteristic
544#107—22no—
545#106—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—41no—
553#102—41no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C4311yescharacteristic
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C4312yes—
593C2×D4C2×D4×C4312yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C4311yescharacteristic
610C22×C4C2×D4×C4311yescharacteristic
611C22×C4C2×D4×C4311yescharacteristic
612C22×C4C2×D4×C4311yescharacteristic
613C22×C4C2×D4×C4311yescharacteristic
614C22×C4C2×D4×C4312yes—
615C22×C4C2×D4×C4312yes—
616C22×C4C24×C4311yescharacteristic
617D8—44no—
618D8—44no—
619M16—44no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—44no—
631C2×C8#41×C4312yes—
632C2×C8#41×C4312yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—81no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C4312yes—
648C4⋊C4C2×D4×C4312yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23#120×C4312yes—
693C23C22×D4×C4311yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4#120×C4312yes—
747C2×C4C22×D4×C4311yescharacteristic
748C2×C4C22×D4×C4311yescharacteristic
749C2×C4C2×#41×C4311yescharacteristic
750C2×C4C2×#41×C4311yescharacteristic
751C2×C4H(5,𝔽2)×C4311yescharacteristic
752C2×C42−1+4×C4311yescharacteristic
753C8—22no—
754C8—22no—
755C8—41no—
756C8—41no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#120×C4311yescharacteristic
786C22C43×#53211yescharacteristic
787C22C43×#53711yescharacteristic
788C22C43×#57611yescharacteristic
789C22C43×#57611yescharacteristic
790C22C43×#57611yescharacteristic
791C22C43×#57711yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C43×#54611yescharacteristic
803C4C43×#54611yescharacteristic
804C4C43×#54711yescharacteristic
805C4C43×#54711yescharacteristic
806C2—42no—
807C2—82no—
808C2—82no—
809C2—161no—
810C2C43×#243011yescharacteristic
811C2C43×#300811yescharacteristic
812C2C43×#301211yescharacteristic
813C2C43×#317611yescharacteristic
814C2C43×#317911yescharacteristic
815C2C43×#325711yescharacteristic
816C2C43×#325911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C43×#540C2semidirect
2. C2×C43×#469C2semidirect
3. C2×C43×#466C2semidirect
4. C43×#2624C2semidirect
5. C43×#2059C2semidirect
6. C43×#2041C2semidirect
7. C43×#2025C2semidirect
8. C43×#2011C2semidirect
9. C43×#1895C2semidirect
10. C43×#1893C2semidirect
11. C43×#1879C2semidirect
12. C43×#1879C2semidirect
13. C43×#1864C2semidirect
14. C43×#1862C2semidirect
15. C43×#1729C2semidirect
348. #25508C43direct (N × H)
398. C2×#540C2×C43semidirect
399. C2×#469C2×C43semidirect
400. C2×#466C2×C43semidirect
401. #2624C2×C43semidirect
402. #2059C2×C43semidirect
403. #2041C2×C43semidirect
404. #2025C2×C43semidirect
405. #2011C2×C43semidirect
406. #1895C2×C43semidirect
407. #1893C2×C43semidirect
408. #1879C2×C43semidirect
409. #1879C2×C43semidirect
410. #1864C2×C43semidirect
411. #1862C2×C43semidirect
412. #1729C2×C43semidirect
471. C43#25508direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C43×#5402
C2×C43×#4692
C2×C43×#4662
C43×#26242
C43×#20592
C43×#20412
C43×#20252
C43×#20112
C43×#18952
C43×#18932
C43×#18792
C43×#18642
C43×#18622
C43×#17292
#2550843